# An object with a mass of #4 kg# is acted on by two forces. The first is #F_1= <4 N , 8 N># and the second is #F_2 = < 1 N, 7 N>#. What is the object's rate and direction of acceleration?

The acceleration is

The resultant force is

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- An object, previously at rest, slides #9 m# down a ramp, with an incline of #pi/6 #, and then slides horizontally on the floor for another #11 m#. If the ramp and floor are made of the same material, what is the material's kinetic friction coefficient?
- A truck pulls boxes up an incline plane. The truck can exert a maximum force of #2,500 N#. If the plane's incline is #(3 pi )/8 # and the coefficient of friction is #1/3 #, what is the maximum mass that can be pulled up at one time?
- If a #4 kg# object moving at #5/2 m/s# slows to a halt after moving #12 m#, what is the coefficient of kinetic friction of the surface that the object was moving over?
- An object with a mass of #8 kg# is on a plane with an incline of # - pi/6 #. If it takes #9 N# to start pushing the object down the plane and #2 N# to keep pushing it, what are the coefficients of static and kinetic friction?
- An object with a mass of #4 kg# is lying still on a surface and is compressing a horizontal spring by #1/4 m#. If the spring's constant is #6 (kg)/s^2#, what is the minimum value of the surface's coefficient of static friction?

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